Question

[(a-b)/(a+b)-(a+b)/(a-b)]÷[1-(a^2+b^2)/(a^2-2ab+b^2)]

Answer 1

[(a-b)/(a+b)-(a+b)/(a-b)]÷[1-(a^2+b^2)/(a^2-2ab+b^2)]
={[(a-b)²-(a+b)²]/(a²-b²)}÷[(a²-2ab+b²-a²-b²)/(a-b)²]
=[(a²-2ab+b²-a²-2ab-b²)/(a²-b²)]÷[-2ab/(a-b)²]
=-4ab/(a-b)(a+b)×(a-b)²/(-2ab)
=2(a-b)/(a+b)
=(2a-2b)/(a+b)

追问

你能把第三步加上括号写清楚吗？

追答

[(a-b)/(a+b)-(a+b)/(a-b)]÷[1-(a^2+b^2)/(a^2-2ab+b^2)]
={[(a-b)²-(a+b)²]/(a²-b²)}÷[(a²-2ab+b²-a²-b²)/(a-b)²]
=[(a²-2ab+b²-a²-2ab-b²)/(a²-b²)]÷[-2ab/(a-b)²]
=[(-4ab)/(a-b)(a+b)]×[(a-b)²/(-2ab)]
=2(a-b)/(a+b)
=(2a-2b)/(a+b)

Answer 2

[(a-b)/(a+b)-(a+b)/(a-b)]÷[1-(a^2+b^2)/(a^2-2ab+b^2)]
=[(a-b)^2-(a+b)^2]/[(a+b)(a-b)]÷{[(a^2-2ab+b^2)-(a^2+b^2)]/(a^2-2ab+b^2)}
=[(a^2-2ab+b^2)-(a^2+2ab+b^2)]/[(a+b)(a-b)]÷[(-2ab)/(a-b)^2]
=(-4ab)*(a-b)^2/[(-2ab)(a+b)(a-b)]
=2(a-b)/(a+b)

Answer 3

[(a-b)/(a+b)-(a+b)/(a-b)]÷[1-(a^2+b^2)/(a^2-2ab+b^2)]